When drawing ellipses, parabolas and hyperbolas, people usually 1) calculate several obvious points first, 2) plot the points on a coordinate axis, and 3) try to eye-ball-fitting these points to form the curve.
There are several downfalls to this procedure. First, people need to calculate at least 4 points on the curve (usually the vertex or foci). And if a better drawing must be obtained, it requires more than just 4 points. Calculating these other points often requires using a calculator; it takes time and is inconvenient. Second, drawing axis and plotting spacing and points can very easily build up errors. Before you know it, the axial unit is not equally spaced, and the points are off. Finally, people rarely draw the curve or connecting the points just once--it never looks good at the first try and often takes several practices. People end up tracing the curve over and over, and the line just becomes very thick. When it becomes messy, people need to erase the curve and start over. And erasing usually makes paper wrinkled or messier. To summarize, it is difficult to obtain a satisfactory graph quickly and conveniently.
In general, free-hand sketching has a negative impact on the quality of a graph. This is why a compass is used to draw circles, and an ellipsograph is used to draw ellipses. These two devices help people to draw very well-defined curves.
Another subject is that telescope mirror-makers use a spherical surface to approximate the ideal parabolic surface. This approximation leads to a poorer image quality.